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作者：Hilario, Marcelo R.; Sa, Marcos; Sanchis, Remy; Teixeira, Augusto
作者单位：Universidade Federal de Minas Gerais; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：Let {& xi;i}i & GE;1 be a sequence of i.i.d. positive random variables. Starting from the usual square lattice replace each horizontal edge that links a site in the ith vertical column to another in the (i + 1)th vertical column by an edge having length & xi;i. Then declare independently each edge e in the resulting lattice open with probability pe = p|e| where p & ISIN; [0, 1] and |e| is the length of e. We relate the occurrence of a nontrivial phase transition for this model to moment proper...
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作者：Deb, Nabarun; Mukherjee, Sumit
作者单位：Columbia University
摘要：In this paper, we study the fluctuations of the average magnetization in an Ising model on an approximately dN regular graph GN on N vertices. In particular, if GN satisfies a spectral gap condition, we show that when-ever dN >> ./N, the fluctuations are universal and the same as that of the Curie-Weiss model in the entire ferromagnetic parameter regime. We give a counterexample to demonstrate that the condition dN >> ./N is tight, in the sense that the limiting distribution changes if dN simi...
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作者：Dario, Paul
作者单位：Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：We study random surfaces with a uniformly convex gradient interaction in the presence of quenched disorder taking the form of a random independent external field. Previous work on the model has focused on proving existence and uniqueness of infinite-volume gradient Gibbs measures with a given tilt and on studying the fluctuations of the surface and its discrete gradient.In this work, we focus on the convergence of the thermodynamic limit, establishing convergence of the finite-volume distribut...
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作者：Schnelli, Kevin; Xu, Yuanyuan
作者单位：Royal Institute of Technology; Institute of Science & Technology - Austria
摘要：We establish a quantitative version of the Tracy-Widom law for the largest eigenvalue of high-dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix X*X converge to its Tracy-Widom limit at a rate nearly N-1/3, where X is an M x N random matrix whose entries are independent real or complex random variables, assuming that both M and N tend to in-finity at a constant rate. This result improves the previous esti...
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作者：Bao, Zhigang; He, Yukun
作者单位：Hong Kong University of Science & Technology; City University of Hong Kong
摘要：In this article, we establish a near-optimal convergence rate for the CLT of linear eigenvalue statistics of N x N Wigner matrices, in Kolmogorov- Smirnov distance. For all test functions f is an element of C5(R), we show that the conver-gence rate is either N-1/2+epsilon or N-1+epsilon, depending on the first Chebyshev coefficient of f and the third moment of the diagonal matrix entries. The condition that distinguishes these two rates is necessary and sufficient. For a general class of test ...
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作者：Coghi, Michele; Nilssen, Torstein; Nuesken, Nikolas; Reich, Sebastian
作者单位：University of Trento; University of Agder; University of London; King's College London; University of Potsdam
摘要：Motivated by the challenge of incorporating data into misspecified and multiscale dynamical models, we study a McKean-Vlasov equation that contains the data stream as a common driving rough path. This setting allows us to prove well-posedness as well as continuity with respect to the driver in an appropriate rough-path topology. The latter property is key in our subsequent development of a robust data assimilation methodology: We establish propagation of chaos for the associated interacting pa...
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作者：Braunsteins, Peter; Den Hollander, Frank; Mandjes, Michel
作者单位：University of Amsterdam; Leiden University - Excl LUMC; Leiden University
摘要：We consider a dynamic Erdo ˝s-Renyi random graph on n vertices in which each edge switches on at rate & lambda; and switches off at rate & mu;, indepen-dently of other edges. The focus is on the analysis of the evolution of the associated empirical graphon in the limit as n & RARR; & INFIN;. Our main result is a large deviation principle (LDP) for the sample path of the empirical graphon observed until a fixed time horizon. The rate is (n), the rate function is a spe-2 cific action integral o...
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作者：Bazaes, Rodrigo; Mukherjee, Chiranjib; Ramirez, Alejandro F.; Saglietti, Santiago
作者单位：Pontificia Universidad Catolica de Chile; Universidad Catolica del Norte; University of Munster
摘要：In 2003, Varadhan (Comm. Pure Appl. Math. 56 (2003) 1222-1245) de-veloped a robust method for proving quenched and averaged large deviations for random walks in a uniformly elliptic and i.i.d. environment (RWRE) on Zd. One fundamental question which remained open was to determine when the quenched and averaged large deviation rate functions agree, and when they do not. In this article we show that for RWRE in uniformly elliptic and i.i.d. environment in d > 4, the two rate functions agree on a...
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作者：Przykucki, Michal; Roberts, Alexander; Scott, Alex
作者单位：University of Birmingham; University of Oxford
摘要：Models of parking in which cars are placed randomly and then move ac-cording to a deterministic rule have been studied since the work of Konheim and Weiss in the 1960s. Recently, Damron, Gravner, Junge, Lyu, and Sivakoff ((2019) Ann. Appl. Probab. 29 2089-2113) introduced a model in which cars are both placed and move at random. Independently at each point of a Cayley graph G, we place a car with probability p, and otherwise an empty parking space. Each car independently executes a random walk...
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作者：Ben Arous, Gerard; Huang, Daniel Zhengyu; Huang, Jiaoyang
作者单位：New York University; Peking University; University of Pennsylvania
摘要：In this paper, we consider the singular values and singular vectors of low rank perturbations of large rectangular random matrices, in the regime the matrix is long: we allow the number of rows (columns) to grow polynomi-ally in the number of columns (rows). We prove there exists a critical signal-to-noise ratio (depending on the dimensions of the matrix), and the extreme singular values and singular vectors exhibit a BBP-type phase transition. As a main application, we investigate the tensor ...
